The bad weather begins tomorrow when city centre shoppers can expect heavy showers in the afternoon and temperatures no higher than 7C (44F).
There's a real chance of snow at the weekend, along with more rain, with the mercury failing to rise above 7C (44F) and dropping to -2C (28F).
Weather forecaster Sean Penston, of MeteoGroup, said tomorrow will be chilly with persistent rain. Showers will be particularly heavy after lunchtime.
He said: "Saturday and Sunday will begin with mist and fog and there will be showers of rain and sleet with a real chance of snow.
"It's unlikely that any snow will lie, however, it will be bitterly cold. The maximum temperature this week will be between 4C (39F) and 7C (44F) while the minimum will be -2C (28F)and 1C (34F)."
It doesn't get much better at the start of next week.
More rain and sleet – with a real possibility of snow – are predicted for Monday and Tuesday with Sean warning it won't be getting any warmer either.
The grim forecast follows a week of plummeting temperatures which brought snow and ice chaos. Track signals at Carstairs and Lanark triggered rail disruptions, while one train had to be taken out of service after its doors froze shut.
Monday also saw thousands of motorists facing snow-covered roads amid criticism that too few gritters had been deployed.
A 12-mile stretch of motorway was reduced to just a single lane on the M74 between Hamilton and Lesmahagow in South Lanarkshire because of the snow.